1. Field of the Invention
This invention relates to an adaptive apparatus for adaptively adjusting parameters in a system.
2. Description of the Related Art
As adaptive systems having functions of adaptively adjusting parameters in a system, There are various kinds of adaptive systems having functions of adaptively adjusting parameters in a system, such as an adaptive control system, an adaptive identification system, an adaptive observation system, an adaptive equalization system and the like. For example, U.S. Pat. No. 4,358,822 discloses an adaptive-predictive control system which carries out a multivariable control of the top and bottom compositions as outputs with reflux and steam flow rates as inputs of a distillation column. This patent further mentions another adaptive-predictive control system applied to single-input single-output control of an aircraft where the pitch angle is controlled by elevator position. In these adaptive systems, the following error equation is used for adjusting parameters. ##EQU1##
In expression (1) described above, e(t) is a scalar error, .zeta.(t) is a usable vector signal, .theta. is an unknown vector parameter, .theta.(t) is an adjustable system parameter as an estimated value of .theta., .psi.(t) is a parameter error having the relationship of .psi.(t)=.theta.(t)-.theta., and s(t) is a usable scalar signal having the relationship of s(t)=.zeta..sup.T (t).multidot..theta..
The adjustable system parameter .theta.(t) must be adjusted so that the following expression (2) is satisfied: ##EQU2##
In a conventional adaptive apparatus, as an adjusting method for this purpose, there has been used a method in accordance with the following expression (3) in which the product of the scalar error e(t) and the vector signal .zeta.(t) is simply normalized to adjust system parameters. ##EQU3##
In another case, there has been used a method in accordance with the following expression (4) in which the product of the scalar error e(t) and the vector signal .zeta.(t) is multiplied by a matrix gain .GAMMA. to adjust system parameters. EQU .theta.(t)=-.GAMMA..zeta.(t)e(t) (4).
Furthermore, in an adaptive system, an error equation such as the following expression (5) may sometimes be used in place of the error equation (1). ##EQU4##
In expression (5), .epsilon.(t) is a scalar error, and an adjustable parameter .theta..sub.t (t) is a vector defined by the following expression (6) using a parameter .theta.(t) conforming to an integral relationship such as expression (3) or (4) and .theta..sub.p (t) conforming to a proportional relationship: EQU .theta..sub.t (t)=.theta.(t)+.theta..sub.P (t) (6).
The parameter .theta..sub.t (t) becomes an adaptive estimation value of .theta..
The adjustable system parameter .theta..sub.t (t) must in general be adjusted so that the following expression (7) is satisfied: ##EQU5##
In an conventional adaptive apparatus, as another adaptive method for this purpose, there has been used a method in accordance with the following expressions (8) and (9) in which the product of the scalar error .epsilon.(t) and the vector signal .zeta.(t) is multiplied by matrix gains .GAMMA. and .GAMMA..sub.P to adjust system parameters: EQU .theta.(t)=-.GAMMA..zeta.(t).epsilon.(t) (8) EQU .theta..sub.P (t)=-.GAMMA..sub.P .zeta.(t).epsilon.(t) (9).
However, in the conventional method in which the system parameter .theta.(t) is adaptively adjusted in accordance with expression (3) described above, the performance of adaptive adjustment is determined when the usable vector signal .zeta.(t) and the scalar error e(t) are obtained, as is apparent from the form of the expression.
In the case of conforming to the above-described expression (4), the performance of adaptive adjustment can be increased by changing the setting of the gain, as is apparent from the form of the expression. Similarly, when the system parameters .theta.(t) and .theta..sub.P (t) are adjusted in accordance with expressions (8) and (9), the performance of adaptive adjustment can also be increased by changing the setting of the gain. In such conventional adjusting methods, however, the gain used for adjustment consists of only a fixed matrix gain which is very limited. Hence, it is impossible to perform appropriate adjustment of parameters having high adaptability.
As a result, since the performance of an adaptive system largely depends on an adaptive apparatus for adaptively adjusting system parameters, it has been impossible to construct an adaptive system which provides excellent performance in conventional apparatuses using the adjusting methods of system parameters as described above.